This is now hosted at www.webfusion.co.uk.
dasBlog is the only engine I found so far, that is built using .Net and does not need a database.
However, I had to do some code changes so that it will work on my shared hosting account.

1. Use of XmlNamespaceUpgradeReader
I changed all occurances of

XmlSerializer ser = new XmlSerializer(typeof(DayExtra),Data.NamespaceURI);
using (StreamReader reader = new StreamReader(fileStream))
{
XmlNamespaceUpgradeReader upg = new XmlNamespaceUpgradeReader( reader, "", Data.NamespaceURI );
DayExtra e = (DayExtra)ser.Deserialize(upg);
}

to

XmlSerializer ser = new XmlSerializer(typeof(DayExtra),Data.NamespaceURI);
using (StreamReader reader = new StreamReader(fileStream))
{

DayExtra e = (DayExtra)ser.Deserialize(reader);
}

The XmlNamespaceUpgradeReader class causes a Security exception, due to a policy implemented by the host.

2. The startup code reads the registry. This is also not allowed. The code accessed the registry to read the time zones available on the server. This code too is disabled. It is now hard coded to the UTC time zone.

Good thing  I had the source code. More power to Open Source. :)